A080825 Triangle read by rows in which n-th row gives trajectory of n (omitting n itself) under the map k -> k-1 if k odd, k -> k/2 if k even.

1, 2, 1, 2, 1, 4, 2, 1, 3, 2, 1, 6, 3, 2, 1, 4, 2, 1, 8, 4, 2, 1, 5, 4, 2, 1, 10, 5, 4, 2, 1, 6, 3, 2, 1, 12, 6, 3, 2, 1, 7, 6, 3, 2, 1, 14, 7, 6, 3, 2, 1, 8, 4, 2, 1, 16, 8, 4, 2, 1, 9, 8, 4, 2, 1, 18, 9, 8, 4, 2, 1, 10, 5, 4, 2, 1, 20, 10, 5, 4, 2, 1, 11, 10, 5, 4, 2, 1, 22, 11, 10, 5, 4, 2, 1, 12, 6, 3

Offset

2,2

Comments

If you write down 0 when divide by 2, 1 when subtract 1, the trajectory gives the binary expansion of n.

Links

Table of n, a(n) for n=2..99.

Example

Triangle begins:
1;
2,1;
2,1;
4,2,1;
3,2,1;
6,3,2,1;
...
7 -> 6 -> 3 -> 2 -> 1, so the 7th row is 6,3,2,1.

Prog

(PARI) xnm1(n, p) = { print1(1" "); for(x=1, n, p1 = x; while(p1>1, if(p1%2==0, p1/=2, p1 = p1*p-1; ); print1(p1" ") ) ) }

Crossrefs

A082404 is a better version.

Sequence in context: A338508 A100380 A205403 * A229724 A034693 A216506

Adjacent sequences: A080822 A080823 A080824 * A080826 A080827 A080828

Keyword

easy,nonn,tabf

Author

Cino Hilliard, Mar 27 2003

Extensions

Edited by N. J. A. Sloane, Dec 06 2008 at the suggestion of R. J. Mathar

Status

approved